Neutral third scales - Revision history

BudjarnLambeth: /* See also */ {{Navbox scale gallery}}

2025-09-28T03:09:45Z

Jdood: /* 24edo */

2025-03-16T05:30:38Z

24edo

← Older revision		Revision as of 05:30, 16 March 2025
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	''Any other scales which contain the 7th (350c) and 14th (700c) degrees of ~~10edo~~ are also considered neutral thirds scales.''		''Any other scales which contain the 7th (350c) and 14th (700c) degrees of 24edo are also considered neutral thirds scales.''

	== See also ==		== See also ==

Lériendil: chromatic pairs link

2024-12-20T05:05:19Z

chromatic pairs link

← Older revision		Revision as of 05:05, 20 December 2024
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	One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma [[243/242]] is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its ''extensions'' (described below).		One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma [[243/242]] is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its ''extensions'' (described below).

	If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[~~Chromatic pairs~~ #Mohaha\|mohaha]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.		If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[Rastmic clan #Mohaha\|mohaha]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.

	Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales #Oktone\|Oktone]], for example.		Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales #Oktone\|Oktone]], for example.

BudjarnLambeth: Add link to orphaned page

2024-12-04T07:12:32Z

Add link to orphaned page

← Older revision		Revision as of 07:12, 4 December 2024
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	''Any other scales which contain the 7th (350c) and 14th (700c) degrees of 10edo are also considered neutral thirds scales.''		''Any other scales which contain the 7th (350c) and 14th (700c) degrees of 10edo are also considered neutral thirds scales.''

			== See also ==
			* [[Songs with neutral intervals]] (not a complete list, only a small sampling)

	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:Neutral\| ]] <!-- main article -->		[[Category:Neutral\| ]] <!-- main article -->
	[[Category:Rastmic]]		[[Category:Rastmic]]

BudjarnLambeth: Added link to 243/242 because it is mentioned a few times throughout the article and readers might want to read about it next

2024-03-13T04:44:02Z

Added link to 243/242 because it is mentioned a few times throughout the article and readers might want to read about it next

← Older revision		Revision as of 04:44, 13 March 2024
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	'''Neutral third scales''' are characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds". It usually refers to a [[MOS]] or [[MODMOS]] generated by a neutral third (usually from 342.9c in [[7edo]] to 360c in [[10edo]]).		'''Neutral third scales''' are characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds". It usually refers to a [[MOS]] or [[MODMOS]] generated by a neutral third (usually from 342.9c in [[7edo]] to 360c in [[10edo]]).

	One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its ''extensions'' (described below).		One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma [[243/242]] is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its ''extensions'' (described below).

	If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[Chromatic pairs #Mohaha\|mohaha]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.		If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[Chromatic pairs #Mohaha\|mohaha]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.

BudjarnLambeth: Merged in content from "neutral scale"

2024-03-12T23:43:58Z

Merged in content from "neutral scale"

@@ Line 138: / Line 138: @@
 * 11/8 LsL: In contrast, two large steps and a small step make a much less consonant and more colorful interval, 11/8.
-== See also ==
+== Lumatone mapping ==
-* [[Lumatone mapping for neutral thirds scales]]
+''See: [[Lumatone mapping for neutral thirds scales]]''.
 [[Category:Lists of scales]]
 [[Category:Neutral| ]] <!-- main article -->
 [[Category:Rastmic]]

BudjarnLambeth at 22:25, 12 March 2024

2024-03-12T22:25:13Z

← Older revision		Revision as of 22:25, 12 March 2024
Line 3:		Line 3:
	One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its ''extensions'' (described below).		One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its ''extensions'' (described below).

	If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[Chromatic pairs #Mohaha\|"mohaha"]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.		If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[Chromatic pairs #Mohaha\|mohaha]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.

	Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales #Oktone\|Oktone]], for example.		Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales #Oktone\|Oktone]], for example.

BudjarnLambeth at 22:24, 12 March 2024

2024-03-12T22:24:55Z

← Older revision		Revision as of 22:24, 12 March 2024
Line 1:		Line 1:
	'''Neutral third scales''' are characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds". It usually refers to a [[MOS]] or [[MODMOS]] generated by a neutral third (usually from 342.9c in [[7edo]] to 360c in [[10edo]]).		'''Neutral third scales''' are characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds". It usually refers to a [[MOS]] or [[MODMOS]] generated by a neutral third (usually from 342.9c in [[7edo]] to 360c in [[10edo]]).

	One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its extensions (described below).		One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its ''extensions'' (described below).

	If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[Chromatic pairs #Mohaha\|"mohaha"]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.		If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[Chromatic pairs #Mohaha\|"mohaha"]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.

BudjarnLambeth: Notes relation to neutral tenperament

2024-03-12T22:24:36Z

Notes relation to neutral tenperament

← Older revision		Revision as of 22:24, 12 March 2024
Line 1:		Line 1:
	'''Neutral third scales''' are characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds". It usually refers to a [[MOS]] or [[MODMOS]] generated by a neutral third (usually from 342.9c in [[7edo]] to 360c in [[10edo]]).		'''Neutral third scales''' are characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds". It usually refers to a [[MOS]] or [[MODMOS]] generated by a neutral third (usually from 342.9c in [[7edo]] to 360c in [[10edo]]).

	One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out.		One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its extensions (described below).

	If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[Chromatic pairs #Mohaha\|"mohaha"]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.		If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[Chromatic pairs #Mohaha\|"mohaha"]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.

BudjarnLambeth: Fixed broken link

2024-03-12T22:21:44Z

Fixed broken link

← Older revision		Revision as of 22:21, 12 March 2024
Line 128:		Line 128:

	== MOSes ==		== MOSes ==
	Neutral third scales are associated with the [[MOS ~~Scales~~\|MOS patterns]] [[3L 4s]] and [[7L 3s]].		Neutral third scales are associated with the [[MOS scales\|MOS patterns]]: [[3L 4s]] and [[7L 3s]].

	In the 3L4s MOS, the large step is a 9/8 and the small step is a 12/11 neutral second. In the 7L3s MOS, the 12/11 is now the large step and the small step is a 33/32 quarter tone.		In the 3L4s MOS, the large step is a 9/8 and the small step is a 12/11 neutral second. In the 7L3s MOS, the 12/11 is now the large step and the small step is a 33/32 quarter tone.

← Older revision		Revision as of 05:05, 20 December 2024
Line 3:		Line 3:
	One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma [[243/242]] is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its ''extensions'' (described below).		One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma [[243/242]] is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its ''extensions'' (described below).

	If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[~~Chromatic pairs~~ #Mohaha\|mohaha]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.		If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[Rastmic clan #Mohaha\|mohaha]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.

	Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales #Oktone\|Oktone]], for example.		Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales #Oktone\|Oktone]], for example.

← Older revision		Revision as of 22:25, 12 March 2024
Line 3:		Line 3:
	One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its ''extensions'' (described below).		One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out, resulting in the [[Rastmic clan#Neutral\|neutral]] temperament and its ''extensions'' (described below).

	If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[Chromatic pairs #Mohaha\|"mohaha"]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.		If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha\|a meantone system]], sometimes called [[Chromatic pairs #Mohaha\|mohaha]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.

	Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales #Oktone\|Oktone]], for example.		Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales #Oktone\|Oktone]], for example.

← Older revision		Revision as of 03:09, 28 September 2025
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	* [[Songs with neutral intervals]] (not a complete list, only a small sampling)		* [[Songs with neutral intervals]] (not a complete list, only a small sampling)


			{{Navbox scale gallery}}
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:Neutral\| ]] <!-- main article -->		[[Category:Neutral\| ]] <!-- main article -->
	[[Category:Rastmic]]		[[Category:Rastmic]]